Intuitively, we expect an accurate MIL predictor \(H\)  to assign large attention weights to the positive images within a positive examination. Then, we select those images whose attention weights are no smaller than a certain threshold, \(t\) . In this work we use \(t = 1/r\) , which corresponds to uniform attention across all \(r\)  images in an examination, but this choice for \(t\)  is not crucial and other options exist.Indeed, since we employ sparse-max [1]}, [2]}, [3]} for the attention mechanism, this behavior is relatively independent of the chosen threshold. Although attention weights are extensively used in recent literature [4]}, [5]}, [6]}, [7]} to select important instances, their theoretical underpinnings remain scarce [8]}, [9]}. On the contrary, the Shapley value [10]} has gained substantial popularity in the machine learning literature [11]} because of its precise theoretical properties. Here, we introduce the first Shapley-based explanation method specifically designed for deep set predictors [12]} (such as the MIL predictor \(H\) ) by extending h-Shap [13]}, a hierarchical extension of the Shapley value (see sec:examlevelhshap for details).h-Shap is available at https://github.com/Sulam-Group/h-shap. Similarly to the attention-based selection method, we select the images which have a Shapley value no smaller than \(t = 1/r\) .
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